Elliptic Curve Group Law
The Group of an Elliptic Curve which has been transformed to the form
is the set of
-Rational Points, including the single Point at Infinity. The grouplaw (addition) is defined as follows: Take 2 -Rational Points 
and 
. Now `draw'a straight line through them and compute the third point of intersection 
(also a -Rational Point). Then 
gives the identity point at infinity. Now find the inverse of
, which can be done by setting 
giving 
.This remarkable result is only a special case of a more general procedure. Essentially, the reason is that this type ofElliptic Curve has a single point at infinity which is an inflection point (the line at infinity meets the curveat a single point at infinity, so it must be an intersection of multiplicity three).
- Eigenvector
- Eight Curve
- Eight-Point Circle Theorem
- Eight Surface
- Eikonal Equation
- Eilenberg-Mac Lane Space
- Eilenberg-Mac Lane-Steenrod-Milnor Axioms
- Eilenberg-Steenrod Axioms
- Ein Function
- Einstein Functions
- Einstein Summation
- Eisenstein Integer
- Eisenstein-Jacobi Integer
- Eisenstein Prime
- Eisenstein Series
- Eisenstein Unit
- Elastica
- Elation
- Elder's Theorem
- Election
- Electric Motor Curve
- Element
- Elementary Function
- Elementary Matrix
- Elementary Operation